- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Spatiotemporal control of charge +1 topological defects in polar active matter

Birte C. Geerds1,2, Abhinav Singh3,4,5, Mathieu Dedenon6,2, Daniel J. G. Pearce2, Frank Jülicher7,1,5,8, Ivo F. Sbalzarini3,4,5,8, and Karsten Kruse6,2,*

  • *Contact author: karsten.kruse@unige.ch
PDF

Phys. Rev. Research 8, 033155 – Published 10 August, 2026

DOI: https://doi.org/10.1103/xc83-kz86

Abstract

Topological defects are a conspicuous feature of active liquid crystals that have been associated with important morphogenetic transitions in organismal development. Robust development thus requires a tight control of the motion and placement of topological defects. In this article, we study a mechanism to control +1 topological defects in an active polar fluid confined to a disk. If activity is localized in an annulus within the disk, the defect moves on a circular trajectory around the center of the disk. Using an ansatz for the polar field, we determine the dependence of the angular speed and the circle radius on the boundary orientation of the polar field and the active annulus. Using a proportional-integral controller, we guide the defect along complex trajectories by changing the active annulus size and the boundary orientation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (40)

  1. J. Prost, F. Jülicher, and J. F. Joanny, Active gel physics, Nat. Phys. 11, 111 (2015).
  2. L. Balasubramaniam, R.-M. Mège, and B. Ladoux, Active nematics across scales from cytoskeleton organization to tissue morphogenesis, Curr. Opin. Genet. Dev. 73, 101897 (2022).
  3. T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, Spontaneous motion in hierarchically assembled active matter, Nature (London) 491, 431 (2012).
  4. H. Gruler, U. Dewald, and M. Eberhardt, Nematic liquid crystals formed by living amoeboid cells, Eur. Phys. J. B 11, 187 (1999).
  5. G. Duclos, S. Garcia, H. G. Yevick, and P. Silberzan, Perfect nematic order in confined monolayers of spindle-shaped cells, Soft Matter 10, 2346 (2014).
  6. T. B. Saw, A. Doostmohammadi, V. Nier, L. Kocgozlu, S. Thampi, Y. Toyama, P. Marcq, C. T. Lim, J. M. Yeomans, and B. Ladoux, Topological defects in epithelia govern cell death and extrusion, Nature (London) 544, 212 (2017).
  7. K. Kawaguchi, R. Kageyama, and M. Sano, Topological defects control collective dynamics in neural progenitor cell cultures, Nature (London) 545, 327 (2017).
  8. P. Guillamat, C. Blanch-Mercader, G. Pernollet, K. Kruse, and A. Roux, Integer topological defects organize stresses driving tissue morphogenesis, Nat. Mater. 21, 588 (2022).
  9. K. Endresen, A. Murali, B. C. Geerds, G. M. Valenzuela Portillo, M. Bloksgaard, D. J. Pearce, and F. Serra, Actuation of cell layers in three dimensions, Adv. Mater. 38, e22191 (2026).
  10. Y. Maroudas-Sacks, L. Garion, L. Shani-Zerbib, A. Livshits, E. Braun, and K. Keren, Topological defects in the nematic order of actin fibres as organization centres of Hydra morphogenesis, Nat. Phys. 17, 251 (2021).
  11. Y. Ravichandran, M. Vogg, K. Kruse, D. J. G. Pearce, and A. Roux, Topology changes of Hydra define actin orientation defects as organizers of morphogenesis, Sci. Adv. 11, eadr9855 (2025).
  12. V. A. Webster-Wood, M. Guix, N. W. Xu, B. Behkam, H. Sato, D. Sarkar, S. Sanchez, M. Shimizu, and K. K. Parker, Biohybrid robots: Recent progress, challenges, and perspectives, Bioinspir. Biomim. 18, 015001 (2022).
  13. D. J. G. Pearce, S. Gat, G. Livne, A. Bernheim-Groswasser, and K. Kruse, Defect-driven shape transitions in elastic active nematic shells, arXiv:2010.13141.
  14. M. M. Norton, P. Grover, M. F. Hagan, and S. Fraden, Optimal control of active nematics, Phys. Rev. Lett. 125, 178005 (2020).
  15. R. Zhang, S. A. Redford, P. V. Ruijgrok, N. Kumar, A. Mozaffari, S. Zemsky, A. R. Dinner, V. Vitelli, Z. Bryant, M. L. Gardel, and J. J. Pablo, Spatiotemporal control of liquid crystal structure and dynamics through activity patterning, Nat. Mater. 20, 875 (2021).
  16. X. Tang and J. V. Selinger, Alignment of a topological defect by an activity gradient, Phys. Rev. E 103, 022703 (2021).
  17. L. J. Ruske and J. M. Yeomans, Activity gradients in two- and three-dimensional active nematics, Soft Matter 18, 5654 (2022).
  18. J. Rønning, M. C. Marchetti, and L. Angheluta, Defect self-propulsion in active nematic films with spatially varying activity, R. Soc. Open Sci. 10, 221229 (2023).
  19. S. Shankar, L. V. D. Scharrer, M. J. Bowick, and M. C. Marchetti, Design rules for controlling active topological defects, Proc. Natl. Acad. Sci. USA 121, e2400933121 (2024).
  20. C. Floyd, A. R. Dinner, and S. Vaikuntanathan, Tailoring interactions between active nematic defects with reinforcement learning, Soft Matter 21, 4488 (2025).
  21. K. Nishiyama, J. Berezney, M. M. Norton, A. Aggarwal, S. Ghosh, Z. Zarei, M. F. Hagan, S. Fraden, and Z. Dogic, Closed-loop control of active nematic flows, Phys. Rev. X 15, 041053 (2025).
  22. S. Ghosh, C. Joshi, A. Baskaran, and M. F. Hagan, Spatiotemporal control of structure and dynamics in a polar active fluid, Soft Matter 20, 7059 (2024).
  23. K. Kruse, J.-F. Joanny, F. Jülicher, J. Prost, and K. Sekimoto, Asters, vortices, and rotating spirals in active gels of polar filaments, Phys. Rev. Lett. 92, 078101 (2004).
  24. K. Kruse, J. F. Joanny, F. Jülicher, J. Prost, and K. Sekimoto, Generic theory of active polar gels: A paradigm for cytoskeletal dynamics, Eur. Phys. J. E 16, 5 (2005).
  25. S. Fürthauer, M. Neef, S. W. Grill, K. Kruse, and F. Jülicher, The Taylor–Couette motor: Spontaneous flows of active polar fluids between two coaxial cylinders, New J. Phys. 14, 023001 (2012).
  26. B. Schrader, S. Reboux, and I. F. Sbalzarini, Discretization correction of general integral PSE operators for particle methods, J. Comput. Phys. 229, 4159 (2010).
  27. P. Incardona, A. Leo, Y. Zaluzhnyi, R. Ramaswamy, and I. F. Sbalzarini, OpenFPM: A scalable open framework for particle and particle-mesh codes on parallel computers, Comput. Phys. Commun. 241, 155 (2019).
  28. A. Singh, P. Incardona, and I. F. Sbalzarini, A C++ expression system for partial differential equations enables generic simulations of biological hydrodynamics, Eur. Phys. J. E 44, 117 (2021).
  29. A. Singh, P. H. Suhrcke, P. Incardona, and I. F. Sbalzarini, A numerical solver for active hydrodynamics in three dimensions and its application to active turbulence, Phys. Fluids 35, 105155 (2023).
  30. A. Singh, L. Kraatz, S. Yaskovets, P. Incardona, and I. F. Sbalzarini, Integrating Odeint time stepping into OpenFPM for distributed and GPU accelerated numerical solvers, J. Open Res. Software 14, 15 (2026).
  31. H. P. Geering, Regelungstechnik: Mathematische Grundlagen, Entwurfsmethoden, Beispiele, 6th ed. (Springer-Verlag, Berlin, Heidelberg, 2013).
  32. P. Guillamat, J. Ignés-Mullol, and F. Sagués, Control of active liquid crystals with a magnetic field, Proc. Natl. Acad. Sci. USA 113, 5498 (2016),.
  33. Z. Zhao, H. Li, Y. Yao, Y. Zhao, F. Serra, K. Kawaguchi, H. Zhang, and M. Sano, Integer topological defects offer a methodology to quantify and classify active cell monolayers, Nat. Commun. 16, 2452 (2025).
  34. S. Coyle, B. Doss, Y. Huo, H. R. Singh, D. Quinn, K. Jimmy Hsia, and P. R. LeDuc, Cell alignment modulated by surface nano-topography—Roles of cell-matrix and cell-cell interactions, Acta Biomater. 142, 149 (2022).
  35. K. D. Endresen, M. Kim, M. Pittman, Y. Chen, and F. Serra, Topological defects of integer charge in cell monolayers, Soft Matter 17, 5878 (2021).
  36. M. Isomäki, C. Fedele, L. Kääriäinen, E. Mäntylä, S. Nymark, T. O. Ihalainen, and A. Priimagi, Light-responsive bilayer cell culture platform for reversible cell guidance, Small Sci. 2, 2100099 (2022).
  37. https://github.com/BertiiG/Spatiotemporal-control-of-charge-1-topological-defects-in-polar-active-matter/tree/main.
  38. A. Singh, A. Foggia, P. Incardona, and I. F. Sbalzarini, A meshfree collocation scheme for surface differential operators on point clouds, J. Sci. Comput. 96, 89 (2023).
  39. L. Giomi, M. J. Bowick, P. Mishra, R. Sknepnek, and M. Cristina Marchetti, Defect dynamics in active nematics, Philos. Trans. R. Soc. A 372, 20130365 (2014).
  40. R. Di Leonardo, S. Keen, F. Ianni, J. Leach, M. J. Padgett, and G. Ruocco, Hydrodynamic interactions in two dimensions, Phys. Rev. E 78, 031406 (2008).

Outline

Information

Phys. Rev. Research 8, 033155– Published 10 August, 2026
  • Received 25 November 2025
  • Accepted 29 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation